To predict the distribution of \(j\)  among dark matter haloes, a large N-body simulation is needed which can model
the acquisition of angular momentum for even the slowest rotating galaxies
in our sample (125 km s\(^{-1}\) ; §3). The simulation we adopt is part of the Horizon Project suite (http://www.projet-horizon.fr).
This follows the evolution of a cubic cosmological volume of 100 \(h^{-1}\)  Mpc on a side (comoving)
containing \(\sim 134\)  million dark matter particles (\(512^3\) ). It starts at \(z=99\)  and is evolved using the publicly
available treecode Gadget 2 [1]} with a softening length of 5 h\(^{-1}\)  kpc (co-moving). The adopted cosmology results in a dark matter
particle mass of \(6.83 \times 10^8 M_{\odot }\) . Dark
matter haloes and the subhaloes they contain are identified with the AdaptaHOP algorithm [2]}.
The halo centres are positioned on the densest dark matter particle
located in the most massive substructure (see [3]} for details).
The total number of haloes and subhaloes in the simulation volume at \(z=0\) 
with more than 100 particles within \(R_{200}\)  and with circular velocities at this radius
which are greater than 100 km s\(^{-1}\)  is 9661.
